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We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and allows to recover ...
In this paper, we propose a novel distributed fault detection method to monitor the state of a-possibly large scale-linear system, partitioned into interconnected subsystems. The approach hinges on the definition of a partition-based distributed Luenberger ...
This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces, W2(Rd). This question arises naturally from the problem of separating amplitude and phase variation i ...
In this thesis we consider inverse problems involving multiscale elliptic partial differential equations. The name multiscale indicates that these models are characterized by the presence of parameters which vary on different spatial scales (macroscopic, m ...
We study the multitype contact process on Z(d) under the assumption that one of the types has a birth rate that is larger than that of the other type, and larger than the critical value of the standard contact process. We prove that, if initially present, ...
Theoretical methods for estimating the bearing capacity of surface strip footings usually do not consider soil-structure interaction. A few publications deal with the subject, but all of these either do not apply rigorous methods or do not consider the gen ...
Several useful variance-reduced stochastic gradient algorithms, such as SVRG, SAGA, Finito, and SAG, have been proposed to minimize empirical risks with linear convergence properties to the exact minimizers. The existing convergence results assume uniform ...
Consider the problem of minimizing a convex differentiable function on the probability simplex, spectrahedron, or set of quantum density matrices. We prove that the expo-nentiated gradient method with Armijo line search always converges to the optimum, if ...
The strong growth condition (SGC) is known to be a sufficient condition for linear convergence of the stochastic gradient method using a constant step-size γ (SGM-CS). In this paper, we provide a necessary condition, for the linear convergence of SGM-CS, t ...
A new strategy based on numerical homogenization and Bayesian techniques for solvingmultiscale inverse problems is introduced. We consider a class of elliptic problems which vary ata microscopic scale, and we aim at recovering the highly oscillatory tensor ...